What’s Your (Math) Problem?! Chapter 1

We are sooooo very excited to welcome each of you to what, we hope, will become a regularly occurring event!  

First things first, let me explain how this will work.  Each week, on Wednesday, you can stop in at one of the blogs listed below.  That blog will have a post up with a link for you to click to take you to that week’s discussion.  We decided that would be the easiest way to keep all the discussion happening in one place and cause the least bit of confusion for all involved (I hope!)  I’ve also listed the dates for each chapter below as a reminder!

Each week one of us will write a quick summary of the chapter and post the questions that NCTM President, Linda Gojak poses in her book to start the discussion.  Then, it’s your turn!  Jump right in and leave your thoughts!  Make sure to use the reply option when replying to a specific person’s thought so that it is easier to follow who is saying what.   The author also suggests keeping a problem-solving journal, or notebook with you as you read, to jot down thoughts and to solve different problems. 

Jennifer Smith-Sloane from 4mulaFun
Meg Anderson  from Fourth Grade Studio
Jamie Riggs from MissMathDork
and Jennifer Findley from Teaching to Inspire 5th Grade


Okay, here we go!  Chapter 1:

What is problem solving?
Gojak begins the chapter by discussing what problem solving is and is not.  What many of his have grown to know as problem solving, both as teacher and as students, is considered routine problem solving.  Routine problem solving is when we, as learners, know how to solve the problem, and really the problem is more an application of a past experience.  Non-routine problem solving, on the other hand, is when learners are given a new task in which they cannot immediately apply something from a past experience to solve the problem.  They MUST make connections to multiple experiences AND extend their thinking and reasoning in order to develop an appropriate answer. Gojak gives an example of the 2 types of problem solving on page 17.  Gojak speaks about students struggling with the non-routine problems.  The struggle is what makes it a true problem, rather than just a task.  (As a teacher, I find that it’s hard to let your students struggle, but if you tell them in advance, “hey you’re going to struggle with this and THAT’S OKAY”, I find that they handle it a bit better)

Why teach problem solving?
Gojak, being the NCTM President, uses the NCTM process standards as her biggest argument for teaching problem solving .  If you are not familiar with the process standards go HERE to read more about them


Who should problem solve? 
Gojak also states that students should begin problem solving as early as pre-school!  I love this idea! By the time the kiddos get to me in middle school they are scared of problem solving… why? because they haven’t done enough of it! Page 27 has a great table of strategies to use for  your kiddos! 

When should we problem solve?
All the time in every math class, every day!  Pages 29 -33 suggest various activities and examples for implementing more problem solving in your classroom.

Where can you find good problems?
And finally, Gojak leaves us with some great website resources! NCTM’s Illuminations is a personal favorite of mine! Check out page 35 and 36 for more problem solving websites (also, feel free to leave your own favorites in the discussion below!)

So, there you have it! Chapter 1, in the books!  Now, let’s “reflect  and act!”  Here are 4 discussions questions that Gojak leaves us with on page 37.  The four of us are looking forward to joining in on a lively discussion with you!  (Also, we are working on a wiki page where we can merge all the information together as a great resource for all of us in the end!)
  1. How is problem solving an important part of your professional growth as a mathematics educator?
  2. How can you convince your students of the importance of problem solving when learning mathematics?
  3. Think about problems you solved in this chapter that involved quantitative reasoning.  Write a description of how you went about approaching and determining a reasonable solution
  4. How has your perspective of problem solving changed after this chapter?

Categories: NCTM and What's Your Math Problem?.

Comments

  1. I thought this first chapter was a great way to introduce the concept of “problem solving.” From a teacher’s perspective, it can be tough to teach this skill because it really isn’t one that can be mastered at once. Problem solving is a skill that is acquired and mastered over time with repetitive practice. Therefore, it must be taught as early as Pre-K and kindergarten and developed throughout elementary school and beyond.

    I agree with Gojak’s statement on p.28 that “problem solving should be a part of every mathematics class.” After I read that sentence, I began to feel overwhelmed as I thought to myself, how do I make sure I incorporate prob solving in EVERY class?!?

    Well, the chart on p. 29-33 was a lifesaver for that question! Gojak provides great examples of times to teach prob solving. (I went a little crazy with my yellow highlighter in this section!)

    So, in conclusion, I guess my perspective of problem solving has changed in that it is more clear to me what prob solving may look like in the classroom, and it is less overwhelming to think about when it comes to including prob solving in my future lesson plans.

    • Mandy, I had the same overwhelming feeling that you spoke about. I LOVED the table and how easy each of her ideas were to use. I also really liked how she not only told you how to use the idea, but gave an example. Concrete examples make the teacher thought process even easier.

      I also like how well Gojak spelled out the idea of problem solving. Problem solving doesn’t just have to be a scary word problem.

      Can you imagine starting problem solving in a district in kindergarten and continuing it each year?! Imagine how second nature problem solving would be if it was embedded into every curriculum on a daily basis.

  2. I am excited about reading this book this summer! One of my favorite take-aways was on p. 25 when Gojak says “The teacher becomes the one who orchestrates the discussion through thoughtful questioning.” I am working on allowing students to discover the math concepts by using high level tasks. I also agree that I need to work on teaching problem solving to my students. I look forward to learning more about problem solving!

  3. I purchased this book in January because it was recommended and I have not had time to read it. A friend of mine gave me the link to this blog and I read chapter 1 and was very excited! I am working on curriculum writing this week and was so happy to see the table with the various ways that problem solving can be used as well as the grade levels they would be most developmentally appropriate for. I too have struggled with making sure I am being a good facilitator for discussing problem solving with and leading my students into being able to discuss problem solving amongst themselves. I can’t wait to read more!! More importantly I cannot wait to implement this next school year.

  4. I am really excited to be reading this book! I, too, loved the chart that gave examples on where to use the different problem solving strategies. I really related to Gojak’s statement on page 27, “Teachers need to be purposeful about the problems and tasks assigned to students.” I am really big on not “spoon feeding” my students. However, I am hoping this book will give me more strategies to help my students become powerful problem solvers. Even if my students understand what a problem is asking, they are afraid of the math necessary to solve it. I am looking forward to seeing what the rest of this book has in store!

    • Erica, Welcome! I’ve read ahead and I think you will find that Gojak does a great job of showing ways to teach without ‘spoonfeeding’. I also think you will be happy with the strategies you learn 🙂

    • Erica, what resource got you started on “not spoonfeeding?”

      Unfortunately, I’ve become the master of spoonfeeding in 3 years of teaching 6th grade. I agree I feel like there’s hope after reading chapter 1. I’m also reading Building Mathematical Comprehension this summer. This is my first summer tackling math now that teaching reading has been “lassoed.”

  5. I had some catching up to do, just got my book this afternoon. Like everyone I’m very excited about the book and the opportunity to bounce things off with others. I want to incorporate more problem solving in my classroom. Love the charts, websites, and the easy feel of the text (easy read). I’m learning a lot and I look forward to learning more.

    • I agree – I enjoy the readability of the text. Too often educational books get caught up in the the words and become overly complicated. I love the look and feel of the book. Easy to read and lots of visual examples – super teacher friendly!

  6. 1.Problem solving is a big part of professional development at this time in my district. We are into Professional Learning Communities which involves problem solving as a team, much like what is being asked of students in order to solve a math problem.

    2. Convincing students of the importance of problem solving is a problem to solve in itself. I teach/serve a low socioeconomic hispanic community using the Holt Math Program. They appear to arrive in sixth grade wanting to practice basic math facts, which they have not mastered. When I receive these students, their problem solving skills are almost non- existent. But as I look around the staff as we switch to common core standards, we are looking around for administration to guide us in traditional methods as well. We need to tackle the problem of our data and solve for low performing students.

    3. As I tackled the problems in chapter 1, I asked myself questions, and tried different strategies. It would have been nice to work with a group on these mathematical questions as well.

    4. My perspective on problem solving has changed in that I know I can use more reading strategies: paraphrasing, summarizing, questioning, etc. I found myself engaged in these strategies as I answer the math related questions. I sure can’t wait to get deeper into this book.

    • 1. B, we do a lot of PLC work at my school too. I’m curious as to how your teachers respond to it?

      2. Balancing teaching the skills with problem solving will be difficult with the students who haven’t mastered them. However, with some practice, and lots of patience, it can work.

      3. I love that you tried different strategies. One of my favorite things to do is work with other teachers to come up with as many creative ways to solve as possible. Sometimes forcing yourself to think like your students introduces some new ideas and helps you think through ways they will struggle.

      4. I’ve been reading the rest of the book and I think you will be quite pleased with what you find!

      Thanks for stopping in and joining the discussion.

  7. I am excited about this book study! At times, I am intimidated when teaching math. It is my hope to learn more than routine strategies to increase the rigor of my instruction. In chapter one I see that there are many more strategies and approaches for teaching mathematics. I am looking forward to learning!

  8. As a remedial math specialist who supports students once or twice a week I know I do not do enough problem solving with my students because of time constraints. I am excited to see what I can glean from this book to start each of our sessions with a problem that would lead to review or teaching of the topic I am to cover that day.

  9. After watching my students struggle with the End of the Year Performance Assessment provided by my district, I knew that something had to change in my approach to Problem Solving in the classroom. I have the students complete a Problem of the Day when they first come in. However, I have noticed that most of the students will sit and do nothing – waiting for me to go over the problem so they could copy down all of the steps necessary to solve the problem.

    Somehow I have to make the students accountable for finding their own way in. I am very encouraged after reading the first chapter that this book and the author’s ideas will help me to make problem solving second nature to my students.

  10. I was very excited to see on Facebook that this book was going to be read with a group of people to discuss it with! Double score! After completing my first year of teaching fifth grade, (I moved down from teaching 7th and 8th Language Arts) I know that problem solving is something that I need to work on with my students. I’m hoping that the book and the discussion generated here will set me on the right path for the fall. Since my book just arrived an hour ago, I will get cracking so I can discuss Chapters One and Two on Wednesday.

Leave a Reply